Article ID Journal Published Year Pages File Type
1896110 Physica D: Nonlinear Phenomena 2014 21 Pages PDF
Abstract
The Keller-Segel system with the logistic growth term is discussed from the spatio-temporal-oscillation point of view. This system exhibits two different types of spatio-temporal oscillations in certain distinct parameter regimes. In this paper, we study the difference between the two types of spatio-temporal oscillations. In particular, the characteristic properties of the behaviors become clear in a limiting system when a certain parameter value tends to zero. Moreover, we demonstrate that the onset of one of the spatio-temporal oscillatory patterns is an infinite-dimensional relaxation oscillation that consists of slow and fast dynamics.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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